One should then analyse
which orbischemes appear in the compactification that this produces (in this paper we
mainly study only smooth orbifolds and their cscK metrics). It is quite possible
that the resulting stable pairs will form a new interesting class.
Studying moduli and stability of varieties using GIT fell out of favour, not least because the singularities it allows are not those that arise naturally in birational geometry,
but interesting recent work of Odaka suggests a relationship between the newer notion
of K-stability (rather than Chow stability) and semi-log-canonical singularities. It
is therefore natural to wonder if orbifold K-stability of \((X,D)\)  is related to some special types of singularity of pairs (perhaps this is most likely in the \(m\rightarrow \infty \) 
limit of the last section). In fact the recent work of Abramovich-Hassett
[1]} precisely studies moduli of varieties and pairs using orbischemes,
birational geometry and the minimal model programme (but not GIT).
